Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities

• Autorzy: Y. Akdim , J. Bennouna , M. Mekkour , H. Redwane
• Języki publikacji: EN

Abstrakty

EN

We study the problem
∂b(x,u)/∂t - div(a(x,t,u,Du)) + H(x,t,u,Du) = μ in Q = Ω×(0,T),
$b(x,u)|_{t=0} = b(x,u₀)$ in Ω,
u = 0 in ∂Ω × (0,T).
The main contribution of our work is to prove the existence of a renormalized solution without the sign condition or the coercivity condition on H(x,t,u,Du). The critical growth condition on H is only with respect to Du and not with respect to u. The datum μ is assumed to be in $L¹(Q)+L^{p'}(0,T;W^{-1,p'}(Ω))$ and b(x,u₀) ∈ L¹(Ω).

Kategorie tematyczne

• 46A32: Spaces of linear operators; topological tensor products; approximation properties
• 47A15: Invariant subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2012
• Tom: 39
• Numer: 1
• Strony: 1-22

Daty

wydano

2012

Twórcy

autor

Y. Akdim

• Département de Mathématiques, Laboratoire d'Analyse Mathématique, et Applications, Faculté des Sciences Dhar-Mahraz, Fès, Morocco

autor

J. Bennouna

• Département de Mathématiques, Laboratoire d'Analyse Mathématiques et Applications, Faculté des Sciences Dhar-Mahraz, Fès, Morocco

autor

M. Mekkour

• Département de Mathématiques, Laboratoire d'Analyse Mathématiques et Applications, Faculté des Sciences Dhar-Mahraz, Fès, Morocco

autor

H. Redwane

• Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1, B.P. 784, Settat, Morocco

Identyfikatory

DOI

10.4064/am39-1-1